You have 100 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.

Note: The length of the sum of three sides is 100. Let w be the width, find the length in terms of w, setup an equation for the area, then find the vertex (maximum) of your equation. Area of rectangle is length * width.

The amount owed at the end of 1 year is $4120 and by the end of 2 years, $4243.60 when Tom borrows $4000 at an interest rate of 3% compounded each year.

The interest you earn on interest is known as compound interest. Simple math can be used to demonstrate this: if you have $100 and it earns 5% interest annually, you will have $105 at the end of the first year. You will end up with $110.25 at the end of the second year. In order to calculate compound interest, multiply the principal of the original loan by the annual interest rate multiplied by the number of compound periods minus one.

Here,

principle amount=$4000

rate of interest=3%

For first year,

A=P(1+r/n)^(nt)

A=4000(1+3/12)^12*1

A=$4,120.00

For first year,

A=P(1+r/n)^(nt)

A=4120(1+3/12)^12*1

A=$4,243.60

When Tom borrows $4000 at an interest rate of 3% compounded annually, the total amount due at the end of one year is $4120, and at the end of two years, it is $4243.60.

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The amount that Kathy got back after 4 years and 6 months is  $3945   .

In the question ,

it is given that ,

the amount invested by Kathy(P) = $3000

the rate at which the amount is invested (r) = 7% per annum

time for which the amount is invested (t) = 4 years and 6 month = 4.5 years

the simple interest calculated by

Simple Interest = ( 3000 × 7 × 4.5)/100

= 94500/100

= 945

So , the interest is $945 .

So , the amount that Kathy get = Principle + Interest

= 3000 + 945

= 3945

Therefore , amount that Kathy got back after 4 years and 6 months is  $3945   .

The given question is incomplete , the complete question is

Kathy invested $3000 at a rate of 7% simple interest for 4 years and 6 months. Find the amount she got back.

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Answer:

which image

Step-by-step explanation:

if you tell me I will answer the question

Answer:

image not found

you can send the image privately

y<2 is the solution to the inequality

What is Linear Inequality?

The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.

The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.

According to the question

2y+3<7

subtracting 3 from both sides

we get,

2y<4

dividing both sides with 2

we get,

y<2

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Answer:

Why is | 330 | the absolute value of the number 330?

The absolute value of a number is how far away the number is from zero. The absolute value is ALWAYS positive.

What is the absolute value of -330?

The negative version of the number is also | 330 |

More Examples

Here are more examples of even and odd numbers in sequence:

Number 328 329 331 332

Absolute Value 328 329 331 332

The solution of the system of equations is , x= -16 - 10/2 = 13

According  to our question-

-2x + 5y = -16  (3) =       -6x + 15y = -48

 3x -  4y  = 17  (2) =         6x -   8y  =   34

7y =     -14

y= -14/7 = 2

-2x + 5(2) = -16

-2x + 10 = -16

x= -16 - 10/2 = 13

hence,The solution of the system of equations is , x= -16 - 10/2 = 13

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The quotient of -0.75 /0.4 is approximately -1.88.

What is the quotient?

This refers to the value you get after division operation has been carried out.

given in the question:

-0.75/0.4 = -1.875

≈ -1.88

Recall, according to the sign rule in mathematics:

Any negative number divided by a positive number gives a negative value.

hence the quotient of -0.75/0.4= -1.875

                                                   ≈ -1.88

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Unit rate is the quantity of an amount of something at a rate of one of another quantity.

3000 miles = 6 hours

4500 miles = 9 hours

The distance asteroid travel in 9 hours is 4500 miles

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

3000 miles = 6 hours

Divide both sides by 6.

500 miles = 1 hour

Multiply 9 on both sides.

9 x 500 miles = 9 hours

9 hours = 4500 miles

Thus,

The distance asteroid travel in 9 hours is 4500 miles

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The percentage increase in cost greater from 2009 is 14.79%

The average price of milk in 2009 = $3.11

The average of price of milk in 2011 = $3.57

The increase in price = The average of price of milk in 2011 - The average price of milk in 2009

Substitute the values in the equation

The increase in price = 3.57 - 3.11

= $0.46

The percentage increase = The increase in price / The average price of milk in 2009 × 100

Substitute the values in the equation

The percentage increase = ( 0.46 / 3.11 )×100

= 14.79%

Hence, the percentage increase in cost greater from 2009 is 14.79%

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Answer: 30$

Step-by-step explanation:

first you divide 420 by 35 and you get 12 times 2.50$ equals 30$

Answer:

Below

Step-by-step explanation:

m = x ( -12b+9)  - 3

m+ 3 = x (-12b+9)

x =   (m+3) / ( -12b+9)       0r     (m+3) / (9-12b)

The equation for the nth term of the arithmetic sequence is  [tex]a_{n}[/tex] = 25 - 4n  

An arithmetic sequence or arithmetic progression is a series of numbers with a common difference. For example 1, 2, 3, 4... is an Arithmetic sequence with a common difference 1. In an Arithmetic sequence, the difference between every two consecutive terms will be equal.

The formula for the nth term of a sequence is given below

=> [tex]a_{n}[/tex] = a + (n-1)d

where a is the first term and d is a common difference.

Here we have

21, 17, 13 ... is the arithmetic sequence

Where first term a = 21

and common difference d = term2 - term1 = 17 - 21 = - 4  

As we know the nth term of AP, [tex]a_{n}[/tex] = a + (n-1)d  

=>  [tex]a_{n}[/tex] = 21 + (n-1)(-4)

=>  [tex]a_{n}[/tex] = 21 - 4n + 4

=>  [tex]a_{n}[/tex] = 25 - 4n

Therefore,

The equation for the nth term of the arithmetic sequence is  [tex]a_{n}[/tex] = 25 - 4n  

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Answer:

a parallel to b

Step-by-step explanation:

I WILL USE SUM OF INTERIOR ANGLES OF A TRIANGLE TO GET x

[tex](2x + 11) + (4x - 5) + 90 = 180 \\ 2x + 4x + 11 - 5 + 90 = 180 \\ 6x + 96 = 180 \\ 6x = 180 - 96 \\ 6x = 84 \\ \frac{6x}{6} = \frac{84}{6} \\ x = 14[/tex]

THE ANSWER IS OPTION a

X=14°

The height of the tower that was supported with the wire is 132.29 feet.

The tower, the wire and the ground would form a right triangle. A right triangle is a polygon that has three sides. The longest side is the hypotenuse. The other two sides are the length and the base.

In this question, the wire is the hypotenuse, the tower is the length and the ground is the base. Pythagoras theorem would be used to determine the height of the tower.

The Pythagoras theorem: a² + b² = c²

where:

a = length

b = base

c = hypotenuse

a² + 150² = 200²

a² + 22,500 = 40,000

a² = 40,000 - 22,500

a² = 17,500

a = √17,500

a = 132.29 feet

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Step-by-step explanation:

that's a right answer u're working on sir appreciated

Answer:

2nd one, hope this helps

Step-by-step explanation:

Answer:

It is C.

Step-by-step explanation:

Do not listen to top answer

I got it right on unit test review ….

The probability that the advertising firm chosen at random has less than $1 million in revenue is 0.56.

The probability that the advertising firm chosen at random has an income between $1 million and $20 million or over $20 million is 0.44.

The rule used is the rule of addition only.

Probability is used in statistics to calculate the likelihood that a random event would take place.  The likelihood that the random event occurs has a probability value that lies between 0 and 1.

The more likely it is that the event would occur, the closer the probability value would be to 1. The more unlikely it is that the event would not happen, the closer the probability value would be to 0.

The rules of addition is used to determine the probability that either of two events would occur.

Probability that the advertising firm chosen at random has less than $1 million in revenue = total number of firms that have a revenue that is less than 1 million / total number of firms surveyed

Probability that the advertising firm chosen at random has less than $1 million in revenue = 148 / 264 = 0.56

Probability that the advertising firm chosen at random has an income between $1 million and $20 million or over $20 million = (number of firms that have an income between $1 million and $20 million / total number of firms) + (number of firms that have an income over $20 million / total number of firms)

= (67 / 264) +  (49 / 264)

= 116 / 264 = 0.44

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Answer:

[tex]y=2x-1[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

A proportion is an equation in which two ratios are set equal to each other and the large sample size required is [tex]0.75[/tex].

What is population proportion?

A fraction is represented in the form of [tex]\frac{a}{b}[/tex], a while ratio [tex]a:b[/tex], then a proportion states that two ratios are equal. Here, [tex]a[/tex] and [tex]b[/tex] are any two integers.

Here, we are determining the minimum sample size for the determination of the population proportion. So, the general formula is of the form is:-

[tex]n=(\frac{z_\frac{x}{2}.x}{E})^{2}[/tex]

Here given values are:-

σ[tex]=76[/tex], population standard deviation

[tex]1-x=0.95\\[/tex], Confidence level

[tex]E=4.5[/tex], Error

Determining the critical value, we get

[tex]z_\frac{x}{2}\\P(z\leq z_\frac{x}{2})=1-\frac{x}{2}\\1-x=0.95\\x=1-0.95\\x=0.05\\\frac{x}{2}=\frac{0.5}{2}\\\frac{x}{2}=0.25\\1-\frac{x}{2}=1-0.25\\\\=0.75[/tex]

Hence, a large sample size is required is [tex]0.75[/tex].

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Answer:

El ciclista recorre en una hora:

18 kilómetros.

Step-by-step explanation:

1 hora = 60 minutos

1 minuto = 1/60 = 0.01667 horas

1 kilómetro = 1000 metros

300 metros = 300/1000 = 0.3 kilómetros

Entonces:

300 metros por minuto = 300metros/minuto

300 metros / minuto = 0.3kilómetros / 0.01667 horas

= 0.3/0.01667

= 18 kilómetros/hora

El ciclista recorre 18 kilómetros cada hora

The horizontal line passing through the point (2, -6) is y = -6 and the vertical line passing through the point (2, -6) is x = 2

We need to write equations for the horizontal and vertical lines passing through the point (2, -6)

For a vertical line the value of x will never change. This will be true for any value of y.

So, the equation for a vertical line passing through this point is:

x = 2

Similarly, for a horizontal line the value of y will never change. This is true for any value of x.

So, the equation for a horizontal line passing through this point is:

y = -6

Therefore, the horizontal line passing through the point (2, -6) is y = -6 and the vertical line passing through the point (2, -6) is x = 2

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There is not any chance of getting negative number in answer.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = 5

Here, f(x) = 5 shows that whatever is the value of x the result value will be 5.

As, there is no variable x in the defined function and only having a constant 5 which is positive in nature.

So, whatever be the value of x is we will get 5  only.

Thus, there is not any chance of getting negative number in answer.

For example, f(1)= 5, f(3)= 5, f(-5)= 5

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Answer:

Step-by-step explanation:

x^-3 * x^-3

Answer:

Step-by-step explanation:

You want the equation of the circle shown on the radar screen as having a radius of 8 miles, centered at the origin.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Your circle is shown as having a radius of 8 miles. It is centered at the same origin where the control tower is located. That means we have ...

  (h, k) = (0, 0)

  r = 8

Using these values in the circle equation gives ...

  (x -0)² +(y -0)² = 8²

It will take 37.5 years.

From the question, we have

A_0 = 8 billion

A  = 9 billion.

r= 3% per year

A  = A_0*e^rt

9 = 8*e^3t/100

9/8 = e^3t/100

Taking log_e both sides,

log_e 9/8 = log_e e^3t/100

9/8 = 3t/100

t = (9*100)/(8*3)

t = 37.5 years

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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